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Question : A dealer sold $\frac{3}{4}$th of his articles at a gain of $24\%$ and the remaining at the cost price. The percentage of gain in the whole transaction is:

Option 1: $15\%$

Option 2:

$18\%$

Option 3:

$24\%$

Option 4:

$32\%$


Team Careers360 6th Jan, 2024
Answer (1)
Team Careers360 24th Jan, 2024

Correct Answer:

$18\%$


Solution : Let the cost price of each article be $\mathrm{C}$.
The dealer sold $\frac{3}{4}$th of his articles at a gain of $24\%$.
The selling price for this part $=\mathrm{\frac{3}{4}C + 0.24 \times \frac{3}{4}C = 0.93C}$
The remaining $\frac{1}{4}$th of the articles were sold at the cost price.
The selling price for this part $=\mathrm{\frac{1}{4}C}$
The total selling price $=\mathrm{0.93C + 0.25C = 1.18C}$
The percentage of gain $=\mathrm{\frac{1.18C-C}{C}×100=18\%}$
Hence, the correct answer is $18\%$.

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